An ellipsis is three dots, or periods, in a row. They can denote a trailing off of a thought, or indicate missing words in a quote.
"Hey guys! What if we... never mind."
If the trailing off comes at the end of a sentence, the ellipsis is followed by a period (four dots at the end).
"Do you think we could...."
If you are trimming down a quote, you use an ellipsis to show something is missing. For example, suppose a politician says, "My colleagues, whom I greatly admire, have decided to vote no." You might trim that down to: "My colleagues [...] have decided to vote no."
Note: For quotes, you use brackets to indicate something you've added - the ellipsis - while the ellipsis represents something missing from the original.
An ellipsis can also be used to indicate a pause longer than a comma. A classic is when Dracula says, "I don't drink... wine."